Abstract

We investigated negative refraction and subwavelength imaging by a mechanically tunable photonic crystal (PC) slab. A honeycomb-structured PC composed of a silicon–polyimide membrane was used because it exhibits isotropic negative refraction within the second photonic band. Using the finite-difference time-domain (FDTD) method, we demonstrated focusing properties of the PC lenses at various frequencies and mechanical stresses. Analyses based on a ray optics model and equifrequency surface also confirmed the behavior observed by the FDTD simulations. These results suggested a mechanically tunable superlens, whose achievable frequency bandwidth was 12.9% of the center frequency for a mechanical stress of ±10%.

Figures (6)

(Color online) (a) Photonic band structure (TM mode) for a two-dimensional (2D) PC with a hexangular structure. The black dashed curve in (a) is the light dispersion curve in air. (b) Ez field patterns for the second band of a triangular lattice of Si rods in polyimide and (c) the second (bottom) and sixth (top) bands of a honeycomb lattice. The hexagonal boundary defines the Wigner–Seitz unit cell.

(Color online) (a) Photonic band structure and (b) EFSs for a 2D PC with a honeycomb structure. Both of them are for TM modes. The black dashed curve in (a) is the light dispersion curve in air. The horizontal red dotted line represents a frequency of 0.309 where the light dispersion curve in air intersects with the second photonic band. (c) The schematic of the honeycomb structure composed of Si rods (with diameter as 0.8a) in polyimide. The lattice orientation Γ–K and Γ–M are also shown.

(Color online) Electric field distribution of point sources and their images across a 2D honeycomb PC slab, at source frequencies of (a) 0.295, (b) 0.300, (c) 0.305, (d) 0.309, (e) 0.315, and (f) 0.320. Red and blue colors are used to represent the positive and negative fields. The locations of the point sources are at a distance of 1.0a0 from the left edge of the slab. Images move away from the PC lenses as the frequency is increased.

(Color online) Electric field distribution of point sources and their images across a 2D honeycomb PC slab for various PC structures at a frequency of 0.305. The PCs are the (a) 5% compressed lattice, (b) 2% compressed lattice, (c) regular honeycomb lattice, (d) 2% stretched lattice, and (e) 5% stretched lattice. The positions of the sources are also at a distance of 1.0a0 from the left edge of the slabs.

(Color online) EFSs of various PC lattices at a frequency of 0.305. They are 5% (the outermost curve) and 2% (second from outside) compressed lattices, regular honeycomb lattice (middle curve), and 2% (second from inside) and 5% (the innermost curve) stretched lattices, which are the same structures we used to perform the FDTD simulation in Fig. 4.

(Color online) Focusing properties vary with PC slabs of different PC structures over a range of frequencies. Besides the regular honeycomb lattice, 2%, 5%, and 10% stretched and compressed lattices were examined as examples. PC structures are represented by curves with different colors and labels. The y axis is the distances between the imaging point and PC slab in the unit of lattice constant a0.